Prepared in cooperation with the 

Connecticut Department of Energy and Environmental Protection

A One-Dimensional Diffusion Analogy Model 

for Estimation of Tide Heights in Selected Tidal 

Marshes in Connecticut

Scientific Investigations Report 2013–5076

U.S. Department of the Interior

U.S. Geological Survey
Cover. Oblique photograph of Sybil Creek Marsh, Connecticut, looking eastward from the mouth of Sybil Creek where it enters Branford 

Harbor, 2003. Courtesy of the Department of Energy and Environmental Protection, Bureau of Water Protection and Land Reuse, and the Office 

of Long Island Sound Programs.
A One-Dimensional Diffusion Analogy 

Model for Estimation of Tide Heights in 

Selected Tidal Marshes in Connecticut

By David M. Bjerklie, Kevin O’Brien, and Ron Rozsa

Prepared in cooperation with the 

Connecticut Department of Energy and Environmental Protection

Scientific Investigations Report 2013–5076

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2013

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Suggested citation:

Bjerklie, D.M., O’Brien, Kevin, and Rozsa, Ron, 2013, A one-dimensional diffusion analogy model for estimation of tide 

heights in selected tidal marshes in Connecticut: U.S. Geological Survey Scientific Investigations Report 2013–5076, 

17 p., http://pubs.usgs.gov/sir/2013/5076/.
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope ..............................................................................................................................3

Study Sites .............................................................................................................................................3

Modeling Method and Calibration ..............................................................................................................3

Method Validation and Application for Sybil Creek .................................................................................9

Validation................................................................................................................................................9

Example Application.............................................................................................................................9

Limitations............................................................................................................................................14

Summary and Conclusions.........................................................................................................................16

Acknowledgments.......................................................................................................................................17

References Cited..........................................................................................................................................17

Figures

1. Map showing locations of Pine Creek, Sybil Creek, Leetes Island, and Wilson Cove 

marshes in Connecticut used for calibration and validation of a one-dimensional 

diffusion analogy model...............................................................................................................2

2. Calibration curve relating the area of the constriction opening that forms the hydromodification to the effective diffusivity of the opening for Pine Creek, Sybil Creek, 

Leetes Island, and Wilson Cove marshes, Connecticut.........................................................8

3. Infrared photograph showing approximate locations of observed and estimated 

elevation points at the boundary of Sybil Creek marsh, Connecticut..................................8

4. Oblique photograph of Sybil Creek marsh, Connecticut, looking eastward from the 

mouth of Sybil Creek where it enters Branford Harbor, 2003..............................................10

5. Photographs of the tide gate in closed position and the bridge constriction on 

Sybil Creek, Connecticut ...........................................................................................................10

6. Map showing areas of water and non-water (land) resulting from MultiSpec 

analysis of the three-band false color infrared orthophotography of Sybil Creek 

marsh, Connecticut ....................................................................................................................11

7. Map showing geographic information system overlay of the Sybil Creek marsh, 

Connecticut, with the channel flow path, perpendicular flow paths from the channel 

to the marsh boundary, and the characteristic marsh polygons defined by buffering 

the perpendiculars and determined by using MutiSpec classification data....................12

8. Graph showing difference between the estimated tide heights and LiDAR heights at 

Sybil Creek marsh, Connecticut, assuming gates closed and using a single point 

calibration, in relation to the distance from the source.......................................................14

9. Infrared photograph showing LiDAR elevations at the boundary of the Sybil Creek 

marsh, Connecticut ....................................................................................................................15

10. Graph showing difference between simulated tide heights, assuming gates-open 

condition, and LiDAR heights at Sybil Creek marsh, Connecticut, in relation to the 

distance from the source ..........................................................................................................16
iv

Tables

1. Calibration results based on data from Sybil Creek, Pine Creek, Lettes Island, and 

Wilson Cove, Connecticut...........................................................................................................6

2. Validation results based on data from Pine Creek, Lettes Island, and Wilson Cove, 

Connecticut....................................................................................................................................7

3. Estimated tide heights and ranges at Sybil Creek, Connecticut, used in the model.......13

Conversion Factors and Datum

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

yard (yd) 0.9144 meter (m)

Area

acre 0.004047 square kilometer (km2

)

square foot (ft2

) 0.09290 square meter (m2)

square inch (in2

) 6.452 square centimeter (cm2)

section (640 acres or 1 square mile) 259.0 square hectometer (hm2

)

square mile (mi2

) 2.590 square kilometer (km2)

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88) and the National Geodetic Vertical Datum of 1929 (NGVD 29).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Elevation, as used in this report, refers to distance above the vertical datum.
A One-Dimensional Diffusion Analogy Model for 

Estimation of Tide Heights in Selected Tidal Marshes in 

Connecticut

By David M. Bjerklie, Kevin O’Brien, and Ron Rozsa

Abstract

A one-dimensional diffusion analogy model for 

estimating tide heights in coastal marshes was developed 

and calibrated by using data from previous tidal-marsh 

studies. The method is simpler to use than other one- and 

two-dimensional hydrodynamic models because it does not 

require marsh depth and tidal prism information; however, 

the one-dimensional diffusion analogy model cannot be used 

to estimate tide heights, flow velocities, and tide arrival times 

for tide conditions other than the highest tide for which it is 

calibrated. Limited validation of the method indicates that it 

has an accuracy within 0.3 feet. The method can be applied 

with limited calibration information that is based entirely on 

remote sensing or geographic information system data layers. 

The method can be used to estimate high-tide heights in tidal 

wetlands drained by tide gates where tide levels cannot be 

observed directly by opening the gates without risk of flooding 

properties and structures. A geographic information system 

application of the method is demonstrated for Sybil Creek 

marsh in Branford, Connecticut. The tidal flux into this marsh 

is controlled by two tide gates that prevent full tidal inundation 

of the marsh. The method application shows reasonable tide 

heights for the gates-closed condition (the normal condition) 

and the one-gate-open condition on the basis of comparison 

with observed heights. The condition with all tide gates open 

(two gates) was simulated with the model; results indicate 

where several structures would be flooded if the gates were 

removed as part of restoration efforts or if the tide gates were 

to fail.

Introduction

Tide gates and ditching are known to affect marine 

estuaries and estuarine habitats by reducing the tidal range, 

decreasing the number of pools, and changing the volume of 

the tidal prism and the inflow and outflow rates (Roman and 

others, 1984; Coats and others, 1989; Roman and others, 1995; 

Giannico and Souder, 2004; Adamowicz and Roman, 2005). 

Decreased flow rates in turn reduce the scouring ability of 

the tidal channel which can hasten sedimentation (Coats and 

others, 1989; Giannico and Souder, 2004). Predicting the tide 

heights inland of tide gates and other hydromodifications (for 

example, constrictions, culverts, and bridges) is an important 

element of planning estuary and marsh restoration, especially 

because dwellings and recreational facilities are often located 

immediately next to the estuary boundary and may be within 

the unobstructed tidal prism with foundations below the 

unobstructed tide height.

In this study, a method was developed for estimating 

tide heights by using a one-dimensional diffusion model. 

The Connecticut Department of Energy and Environmental 

Protection (CTDEEP) has identified nine priority wetlands 

as being substantially affected by tide gates; therefore, an 

investigation of improved methods for understanding the 

effects of hydromodifications was undertaken. For this study, 

conducted by the U.S. Geological Survey (USGS) in cooperation with the CTDEEP, two of those sites were included in the 

analysis (Sybil and Pine Creeks), along with two non-priority 

sites that have sufficient data for the analysis. The locations 

of the four sites are shown in figure 1. The method developed 

during the study uses observed tide heights downstream and 

upstream from the tide gates, tide height within the marsh, and 

hydraulic modeling to estimate the high-tide height for any 

given design or regulatory tidal range. Readily available geospatial source information (at a minimum, orthophotography) 

and limited calibration data were used. The method does not 

require detailed information about the depth of the tidal marsh 

or extensive field data collection, and estimates can be made 

from available geographic information system (GIS) data with 

minimal expense.

The method can be used as a guide to assist in land-use 

planning and wetland restoration, or to identify and quantify 

risks to development in or adjacent to the coastal floodplain 

from future tidal floods or gate failures. The method could 

lead to a more accurate and consistent estimation of the limits 

of extreme high water for use by managers, engineers, and 

other interested parties.

Estimates developed from the method can be used as 

a guide to determining when changes, impingement, and 

alterations to the marsh upstream from tide gates require 

state permits and to help property owners realize that they are 

proposing development in the coastal floodplain that could be 

damaged by future spring tidal floods or gate failure.
2 A One-Dimensional Diffusion Analogy Model for Estimation of Tide Heights in Selected Tidal Marshes in Connecticut Guilford Madison Fairfield Milford Norwalk Branford Orange Clinton Westport Darien New Haven Bridgeport Westbrook Old Lyme Stratford Old Saybrook East Haven West Haven Stamford 72°30' 73° 73°30' 41°40' 41°20' 41° CONNECTICUT Inset area

Long Island Sound

Connecticut River

Housatonic River

Wilson

Cove

Pine Creek

Sybil Creek

Leetes Island

Branford

Harbor

Bridgeport

Harbor EXPLANATION

Marsh area

Town boundary

0 5

0 5

10 MILES

10 KILOMETERS

Base map from U.S. Geological Survey, 1969–1984, 1:24,000 (digitized)

Figure 1. Locations of Pine Creek, Sybil Creek, Leetes Island, and Wilson Cove marshes in Connecticut used for calibration and validation of a onedimensional diffusion analogy model.
Modeling Method and Calibration 3

Purpose and Scope

This report describes the one-dimensional diffusion analogy model used to estimate tide heights in marshes with tide 

gates. Calibration and validation are described, and the data 

used for calibration and validation of the model are presented 

in tables. An example application of the method is presented.

Study Sites

This study used data from four previously studied tidal 

marshes to develop and calibrate the model. The sites are 

located on the Connecticut shoreline along Long Island Sound 

and include Pine Creek in Fairfield, Sybil Creek in Branford, 

Wilson Cove in Norwalk, and Leetes Island Cove in Guilford. 

Pine Creek and Sybil Creek (fig. 1) are two of the CTDEEP 

priority marshes; both contain more than one constricted opening, including tide gates, channelization, culverts, and bridges. 

The two other marshes used in this study, Leetes Island and 

Wilson Cove, do not have developed areas in the floodplain 

but provided a range of values that could be used to develop 

calibration relations between the size of the opening and the 

attenuation of the tidal surge.

Three of the marshes were studied by the consulting 

firm Milone and MacBroom: Sybil Creek in 1987, Leetes 

Island in 1999, and Wilson Cove in 1999 (Milone and 

MacBroom Consulting Engineers, 1987, 1999a, 1999b, 

respectively). These studies included tidal monitoring and 

mapping of the marsh; the Leetes Island study also included 

a two-dimensional modeling application as part of a marsh 

restoration study. Pine Creek marsh was studied by the USGS 

(Larry Weiss, U.S. Geological Survey, written commun., 

1992); tidal monitoring and assessment of the marsh response 

to the tide were part of a preliminary study for the Town 

of Fairfield, Conn. The preliminary study was designed to 

assess the feasibility of developing a hydrodynamic model of 

the marsh. 

Each of the study marshes had available tide-height 

information and mapping that was used to characterize 

the hydraulic conditions in the main tidal channels and 

in the vegetated marsh areas. The four marshes were 

visited by USGS personnel for the current study, and the 

hydromodifications (in the form of constrictions to flow at 

culverts) were observed and measured for opening size and 

general hydraulic conditions.

All of the marshes, except Wilson Cove, have tide gates 

that operate with varying levels of efficiency. Pine Creek and 

Sybil Creek each have more than one hydromodification—

constricted bridge openings and open culverts—in addition 

to the tide gates. The tide gates at Sybil Creek consist of 

two approximately 4-foot by 4-foot openings. Under normal 

operating conditions with the gates closed, ponds and salt 

pannes in the Sybil Creek marsh show small or negligible tidal 

flux, indicating that they are isolated or above the height of the 

tidal flux. The leakage through the gates is greatly reduced (as 

of 2010) compared to leakage when Milone and MacBroom 

(1987) did their study. However, during the Milone and 

MacBroom study (1987), one of the gates was opened to allow 

for observation of tidal flux at various points in the marsh. 

Both gates could not be opened because the resulting tidal 

flood threatened to inundate adjacent properties. The other 

three marshes all show tidal flux within the marsh. The tide 

gates at Pine Creek consist of two 4-foot-diameter circular 

gated culverts that were open at the time of the earlier USGS 

study (Larry Weiss, U.S. Geological Survey, written commun., 

1992). Leetes Island has a single, gated 3.5-foot-diameter 

culvert that was open at the time of the Milone and MacBroom 

study (1999a). Wilson Cove marsh is connected to Long Island 

Sound by twin 6-foot-diameter corrugated metal pipes with 

no gates.

Modeling Method and Calibration

A relatively simple method to estimate tide heights 

in marshes has been developed that can be used in regions 

and with scenarios in which tide heights cannot be directly 

measured. The objectives are to use readily available data and 

apply the method to any marsh with relatively small effort. 

This simplified, one-dimensional diffusion model was developed, tested, and used to derive tide heights at the boundary 

of a marsh. The method was designed to be easily adaptable 

to other regions of the coast, and it requires only planimetric 

marsh geometry and the size of the gate opening (leakage) to 

define the relation between downstream and upstream tidal 

events. Because this approach does not consider the tidal 

prism (volume) explicitly, the flood height is transferred inland 

without attenuation resulting from storage, except as a consequence of a calibration of the diffusion coefficient. Therefore, 

the method is considered to provide a conservative estimate 

(the highest potential height).

Other modeling methods that have been used to estimate 

tide heights in estuaries include one and two dimensional analytical and numerical solutions to unsteady flow equations that 

are based on flow resistance (momentum) and conservation 

of mass (Roman and others, 1995; Coats and others, 1989). 

These models require channel and marsh depth and calibrated 

flow resistance coefficients. In comparison, the method developed in this report requires a calibrated diffusivity coefficient 

but does not require measured or estimated flow depth as input 

to the model. In effect, the diffusivity coefficient incorporates 

flow resistance and depth into a single calibration. Because of 

this, the model presented here can be calibrated and applied by 

using only planimetric information available from maps and 

readily available geospatial data (orthophotography, GIS data 

layers) However, the diffusion model presented here is not a 

complete representation of the marsh geometry; it provides 

a potential height value as a function of distance, tidal range, 

and diffusive characteristics. 

The model employs a one-dimensional harmonic function 

using a diffusion analogy adapted from a method to estimate 

the effect of tides on groundwater levels (Turner and others, 
4 A One-Dimensional Diffusion Analogy Model for Estimation of Tide Heights in Selected Tidal Marshes in Connecticut

1996; Todd, 1980, p. 242–247; Ferris, 1951). This method 

was used to estimate the attenuation of a periodic wave (tide) 

with distance and over time within a marsh. For this method, 

which incorporates Darcy’s Law (Todd, 1980, p. 242–247), it 

is assumed that flow conditions are laminar, velocity head is 

minimal (low Reynolds number), and there is a linear proportionality between flow resistance and head loss and an inverse 

proportionality between flow and length of the flow path. 

These assumptions are reasonable for the marsh because the 

flow is contained within the spaces between the marsh vegetation (analogous to flow in porous media), but flow may not be 

contained in the open channels and constricted openings to the 

marsh, such as inlet culverts.

Some of the hydraulic issues that may arise as a result of 

flow in the channels and culverts include change in flow resistance as flow depth changes and head differences upstream 

and downstream from constrictions. Because of these hydraulic issues, the model is calibrated only for the high-tide level 

of interest. Predictions for tidal conditions at less than high 

tide are not considered calibrated and may not be reasonable.

The basic diffusion equation is

∂

∂ = ∂

∂

2

2

h

x

D h

t f , (1)

where

Df is the diffusion coefficient (hereafter referred 

to as the diffusivity with units of time 

divided by length squared, T/L2);

h is the volumetric height (L);

t is time (T); and

x is volumetric length (L).

This equation can be readily developed from the onedimensional transient equation of continuity and a onedimensional equation of motion. The transient equation for 

continuity (Turner and others, 1996) is

∂

∂ = ∂( )∂

h

t S

hv

x x

1 , (2)

where

Sx is the storativity of the volume (the available 

storage in the volume, dimensionless); and

v is the net flow velocity out of the volume 

(L/T).

An equation of motion for laminar flow, provided by 

Darcy’s law (Turner and others, 1996; Todd, 1980, p. 242–

247), is

v K dh

dx = , (3)

where

K is the conductance coefficient (hydraulic 

conductivity, L/T).

Darcy’s law is a simple representation of a flow 

resistance equation that assumes a linear response to changes 

in head (depth). Fick’s Law (Fisher and others, 1979) is 

identical in form to Darcy’s Law and results in the classic onedimensional diffusion equation (eq. 1). As such, the method 

used here is a mass diffusion equation for movement of water 

into the marsh.

Substituting Darcy’s law (eq. 3) into equation 2 results in

∂

∂ =

∂

∂

h

t S

Kh dh

dx

x x

1 ( ) . (4)

Simplifying with Kh equal to the transmissivity, T (L2/T),

∂

∂ = ∂

∂

h

t

T

S

h

x x

2

2 . (5)

A comparison of equations 1 and 5 shows that, in this 

application, the diffusivity (as defined for eq. 1) for the marsh 

is equivalent to the inverse of the ratio of transmissivity to 

storativity. The transmissivity values are assumed to be very 

high for open water and much smaller for the vegetated marsh; 

similarly, the storativity is assumed to range from 1 for open 

water to a fraction for the vegetated marsh. Relating the diffusivity to the transmissivity and storativity provides a means 

to estimate the diffusivity from estimated hydraulic properties 

of the marsh characteristics.

Assuming the boundary conditions of a periodic change 

in head at the outlet of the marsh are represented by a sine 

function for the daily tidal flux and that at h = 0, x = ∞, the 

solution to equation 5 is (Ferris, 1951; Todd, 1980, p. 242–

247; and Turner and others, 1996)

h h e

D

t x

x f = −

0

0

 (6)

and

t x

t D

L

f = 0

4 , (7)

where

hx is one-half the maximum tidal amplitude at 

distance x from the source, in feet;

h0 is one-half the maximum tidal amplitude at 

source, in feet;

x is distance from tidal source, in feet;

t

0 is tidal period, per day;

t

L is the time (lag time) required for hx

 to be 

reached relative to the source, per day;

Df is diffusivity, per day per square feet; and

π is the ratio of the circumference to the 

diameter of a circle.
Modeling Method and Calibration 5

A value for Df was calibrated for channel and marsh 

distances between known points of tide height with equation 2 

by matching the tide-height observations. The approach used 

here is to measure the travel length (distance) on a map along 

the open channel; then, to estimate a travel length through the 

marsh, draw a straight line perpendicular to the flow path from 

the channel out into the marsh. The calibration of the model 

was achieved by fitting the best value for diffusivity, given 

the measured lengths that result in the observed tide heights. 

Through this procedure, values of diffusivity for the vegetated 

marsh and channel environments were determined. On the 

basis of the calibration, the range of diffusivity values for the 

open channel and the marsh tended to be similar at the different sites (see tables 1 and 2), low for the vegetated marsh and 

very low for the open water.

The assumption of a linear response between head change 

and flow resistance requires that flow resistance does not 

change with head, implying that friction is uniform. Considering tidal flow into the marsh through the marsh vegetation, 

this assumption may be reasonable; however, it is not necessarily reasonable for flow in the open channels of the marsh 

and through the constricted opening to the marsh, such as a 

culvert. These issues are addressed through calibration of the 

diffusivity, but the calibration, therefore, applies only to a 

specific flow condition; in this study, that flow condition is the 

high tide. Lower tide heights cannot be relied upon; therefore, 

the time of arrival may have substantial errors as a result of 

improper accounting for the time of travel at lower tide levels.

Similarly, Df was calibrated for channel sections with 

constrictions, including tide gates, bridges, and culverts. The 

diffusivity estimated for the constrictions was determined as 

described above for the channel and marsh. Where the marsh 

is broken into different regions by in-line structures, a model 

was derived for each region, and models were used in series 

(a link-node type model). For locations with more than one 

structure at a constriction, all of the structures were modeled 

with a constant diffusivity. 

A relation was derived between the size of the opening 

at each constriction and the calibrated diffusivity through 

the constriction for all four study sites (fig. 2). The crosssectional areas shown in figure 2 reflect the hydromodification 

caused by the opening size of the constriction; however, the 

diffusivity value accounts for the effects of the length of the 

culvert and channel positioned between the calibration points. 

These effects are assumed to be small relative to the effect 

of the opening. Thus, the curve shown is applicable to the 

data in this study but is not a general relation, and provides 

a means to estimate a change in diffusivity given alternative 

or hypothetical opening sizes (for example, gates fully open, 

gates closed, gates half open). In the future, a more general 

relation between dimensionless scalars could be developed 

to characterize openings and diffusivity, such as opening 

diameter divided by culvert length and opening area divided 

by area of the inflow channel. The small data set available here 

precluded a more in-depth analysis. 

Recognizing the limited data used to develop the relation 

between the diffusivity (Df  ) and the constricted opening, the 

sensitivity of the model to different values for the Df and travel 

length (x) was assessed. Doubling of Df results in a 12-percent 

increase in the simulated tidal height (hx); halving Df results 

in a -15-percent change in hx (it is a log function such that the 

larger the change in Df the less change in hx). The hx is also 

sensitive to the travel length (x) over which Df is applied; the 

shorter the x, the less error is introduced by a different Df.

The high-tide height is based on the simulated attenuation 

of the tidal amplitude determined using equation 6. The height 

of the high tide is determined from the estimated height relative to the tidal datum. The length of time for the arrival of the 

high tide (lag time, calculated from eq. 7) was not used as a 

calibration criterion but serves as a verification of the method.

The results of the calibration for all four marshes are 

shown in table 1. Approximate locations of the observed and 

estimated tide heights and the location of structures for Sybil 

Creek marsh, a typical marsh, are shown in figure 3. The tide 

heights were fit by adjusting the diffusivity and thus are in 

good agreement with the observed heights. This method can 

be used to estimate tidal range, peak tide height, and lag times 

to the peak height.

The lag times were not used in the calibration and thus 

serve as a qualitative validation of the method. The lag-time 

estimates are not considered to be as accurate as the tideheight estimates because (1) the actual flow path is unknown 

(and not simulated) and thus may differ from the assumed 

path as represented by the flow length in the simulation and 

(2) the calibration is for the high tide only with no representation of the time needed for water to move into the marsh at 

intermediate tide heights. Where lag times are available for 

comparison, the method provides reasonable values for the 

sites, with the exception of Wilson Cove, where the estimated 

lag times and observed lag times are an order of magnitude 

different. The reason for this may be that there are large storage effects in this marsh; however, it does not seem reasonable 

that the observed lag time at station 2c (fig. 3), which is only 

25 feet (ft) from the edge of the channel, requires an observed 

time of 34 minutes for the tide to travel from the source 280 ft 

downstream. This indicates that there may be an issue with the 

time stamp for the observed values relative to the timing of 

the tidal cycle. Alternatively, the model may not appropriately 

represent the travel path or physical characteristics associated 

with this marsh.

The lag time is a function of distance, diffusivity, and the 

tidal period but not the tidal range or height (eq. 7). Thus, for 

a given point in the marsh, given the same geometric conditions governing diffusivity and distance, the lag time should be 

the same for a given tidal period. The model shows this result, 

although it is best to keep in mind that the lag time does not 

reflect time on a clock, and it is assumed that the tidal period 

remains constant. Because the timing and height estimates 

are derived from the length and diffusivity values, the tide 

heights can be mapped in two dimensions given an appropriate 

scheme for assigning the diffusivity and travel length to any 

point of interest within the marsh.
6 A One-Dimensional Diffusion Analogy Model for Estimation of Tide Heights in Selected Tidal Marshes in Connecticut

Table 1. Calibration results based on data from Sybil Creek, Pine Creek, Lettes Island, and Wilson Cove, Connecticut.

[The observation station designations are taken from the site studies (Milone and MacBroom, 1987; Larry Weiss, U.S. Geological Survey, written commun., 1992; 

Milone and MacBroom, 1999a; Milone and MacBroom, 1999b). The letter c denotes that the station is in a channel, and the letter m denotes that the station is in 

the marsh. Elevations are in feet above the National Geodetic Vertical Datum of 1929; ft, feet; min, minutes; --, no data; t0, tidal period; Df, diffusivity; 

ft2, square feet; h0, 1⁄2 the tidal amplitude; hx, 1⁄2 the tidal amplitude at distance x from the tidal source; tL, the time lag required for hx to be reached. Variables correspond to equations 6 and 7]

Observation 

station

Distance of 

segment x 

(ft)

t

0

(day)

Df

(day/ft2)

Variables

h0

(ft)

hx

(ft)

Estimated 

height 

(ft)

Observed 

height 

(ft)

Difference between 

estimated and 

observed heights 

(ft)

t

L

 estimated 

(min)

t

L

 observed 

(min)

Sybil Creek 14-July, 1987

P2 700 0.5 5.26E-08 7 4.68 3.01 3.02 -0.01 46.13 45

P3 875 0.5 2.63E-08 4.68 3.28 2.11 2.11 0 86.9 60

S1c 800 0.5 5.00E-12 4.68 4.66 3 -- -- 46.64 --

S1m 400 0.5 1.25E-07 4.66 3.27 2.1 2.1 0 86.75 --

S2c 1,350 0.5 5.00E-12 3.28 3.25 2.09 -- -- 87.77 71

S2m 150 0.5 5.00E-07 3.25 2.49 1.6 1.61 -- 118.23 90

Pine Creek 22-June, 1992

Dam Road 1,750 0.5 3.33E-14 5.6 5.6 4.1 4.1 0 -- --

Salt Meadow 6,550 0.5 8.33E-12 5.6 5.34 3.91 3.9 0.01 -- --

Old Field 2,000 0.5 4.76E-10 5.34 4.78 3.5 3.5 0 -- --

Leetes Island 19-Mar., 1999

Sta2 170 0.5 5.43E-06 6 2.22 1.63 1.63 0 113.84 140

Sta3 1,200 0.5 1.00E-10 2.22 2.16 1.58 1.58 0 117.28 --

Sta4c 1,930 0.5 10.00E-12 2.22 2.19 1.6 -- -- 119.04 --

Sta4m 150 0.5 8.33E-09 2.19 2.11 1.55 1.55 0 122.97 180

Sta5c 1,430 0.5 10.00E-12 2.22 2.2 1.61 -- -- 120.34 --

Sta5m 300 0.5 5.00E-09 2.2 2.08 1.53 1.53 0 126.43 --

Wilson Cove 7-Oct., 1999

Sta2c 240 0.5 3.33E-09 8.99 8.68 5.79 5.78 0.01 3.98 --

Sta2m 25 0.5 2.50E-08 8.68 8.6 5.73 5.72 0.01 5.12 34

Sta3 (at culvert) 530 0.5 3.33E-12 8.68 8.66 5.77 5.77 0 4.26 55

Sta5 450 0.5 5.00E-11 8.66 8.59 5.73 5.72 0.01 5.17 59

Sta6 65 0.5 3.33E-09 8.59 8.51 5.67 5.67 0 6.25 50

Sta7 (at culvert) 1,320 0.5 1.67E-11 8.66 8.55 5.69 5.69 0 6.72 62
Modeling Method and Calibration 7

Table 2. Validation results based on data from Pine Creek, Lettes Island, and Wilson Cove, Connecticut.

[The observation station designations are taken from the site studies (Milone and MacBroom, 1987; Larry Weiss, U.S. Geological Survey, written commun., 

1992; Milone and MacBroom, 1999a; Milone and MacBroom, 1999b). The letter c denotes that the station is in a channel, and the letter m denotes that the station 

is in the marsh. Elevations are in feet above the National Geodetic Vertical Datum of 1929; ft, feet; min, minutes; --, no data; t0, tidal period; Df, diffusivity; 

ft2, square feet; h0, 1⁄2 the tidal amplitude; hx, 1⁄2 the tidal amplitude at distance x from the tidal source; tL, the time lag required for hx to be reached. Variables correspond to equations 6 and 7]

Observation 

station

Distance of 

segment x 

(ft)

t

0

(day)

Df

(day/ft2)

Variables

h0

(ft)

hx

(ft)

Estimated 

height 

(ft)

Observed 

height 

(ft)

Difference between 

estimated and 

observed heights 

(ft)

t

L

 estimated 

(min)

t

L

 observed 

(min)

Leetes Island 7-Apr., 1999

Sta2 170 0.5 5.43E-06 5 1.85 1.26 1.55 -0.29 113.84 95

Sta3 1,200 0.5 1.00E-10 1.85 1.8 1.22 1.5 -0.28 117.28 --

Sta4c 1,930 0.5 10.00E-12 1.85 1.82 1.24 -- -- 119.04 --

Sta4m 150 0.5 8.33E-09 1.82 1.76 1.2 1.4 -0.2 122.97 180

Sta5c 1,430 0.5 10.00E-12 1.85 1.83 1.24 -- -- 120.34 --

Sta5m 300 0.5 5.00E-09 1.83 1.74 1.18 1.45 -0.27 126.43 --

Leetes Island 16-Apr., 1999

Sta2 170 0.5 5.43E-06 4.45 1.65 1.28 1.5 -0.22 113.84 55

Sta3 1,200 0.5 1.00E-10 1.65 1.6 1.24 1.33 -0.09 117.28 --

Sta4c 1,930 0.5 10.00E-12 1.65 1.62 1.26 -- -- 119.04 --

Sta4m 150 0.5 8.33E-09 1.62 1.57 1.22 1.25 -0.03 122.97 115

Sta5c 1,430 0.5 10.00E-12 1.65 1.63 1.26 -- -- 120.34 --

Sta5m 300 0.5 5.00E-09 1.63 1.54 1.2 1.3 -0.1 126.43 --

Wilson Cove 23-Sep., 1999

Sta2c 240 0.5 3.33E-09 5.5 5.31 4.67 -- -- 3.98 --

Sta2m 25 0.5 2.50E-08 5.31 5.26 4.63 -- -- 5.12 --

Sta3 (at culvert) 530 0.5 3.33E-12 5.31 5.3 4.66 4.73 -0.07 4.26 35

Sta5 450 0.5 5.00E-11 5.3 5.26 4.63 4.66 -0.03 5.17 71

Sta6 65 0.5 3.33E-09 5.26 5.21 4.58 4.67 -0.09 6.25 45

Sta7 (at culvert) 1,320 0.5 1.67E-11 5.3 5.23 4.6 4.67 -0.07 6.72 58

Pine Creek 21-June, 1992

Dam Road 1,750 0.5 3.33E-14 5.4 5.4 4.1 4.05 0.05 -- --

Salt Meadow 6,550 0.5 8.33E-12 5.4 5.15 3.91 3.7 0.21 -- --

Old Field 2,000 0.5 4.76E-10 5.15 4.61 3.5 3.45 0.05 -- --
8 A One-Dimensional Diffusion Analogy Model for Estimation of Tide Heights in Selected Tidal Marshes in Connecticut

y = 5.2048x-6.591

R2 = 0.9077

1E-11

1E-09

0.0000001

0.00001

0.001

0 10 20 30 40 50 60

Diffusivity, in day per feet squared

Area of the restriction opening, in square feet

Leetes Island

Sybil Creek

Pine Creek

Wilson Cove

EXPLANATION

Figure 2. The area of the constriction opening that forms the hydromodification to the effective diffusivity of 

the opening for Pine Creek, Sybil Creek, Leetes Island, and Wilson Cove marshes, Connecticut.

Tide Gate

Bridge

P2

P3

S1m

S2m

S1c S2c

Elevation points at marsh boundary

EXPLANATION

Site locations and identifier

250 500 METERS

2,000 FEET

0

0 1,000

Figure 3. Approximate locations of observed and estimated elevation points at the boundary of Sybil Creek marsh, 

Connecticut.
Method Validation and Application for Sybil Creek 9

Method Validation and Application for 

Sybil Creek

The method was validated by applying it to the four 

marshes by using different dates for which observed tide 

heights were available. The method was applied to the Sybil 

Creek marsh to estimate the high-tide elevation around the 

perimeter of the marsh.

Validation

The method was validated by using the calibrated values 

for diffusivity to estimate tide heights in Leetes Island marsh, 

Wilson Cove marsh, and Pine Creek marsh for days not 

used in the calibration and comparing the estimates against 

observed heights. In most cases, the data used for validation 

were separated by more than a few weeks from the data used 

for calibration. This could not be done with the Sybil Creek 

marsh because observations were made on 1 day only during 

the study period. The results of the validation test are provided 

in table 2. On the basis of this validation, the method accuracy averages about ±0.1 to 0.2 foot with a maximum error 

of 0.3 foot (the largest error between simulated and observed 

tide heights). The model had a tendency to under predict tide 

heights at all sites, except Pine Creek. Given the small number 

of sites and the consistent range of error (positive or negative), 

it was not feasible to evaluate whether there is any relation 

between marsh characteristics and error.

Example Application

The method was tested for Sybil Creek in Branford, 

Conn., by using a GIS application to estimate tide heights 

at the upland edge of the eastern portion of the Sybil Creek 

marsh, which is shown on figure 4. The application extended 

the estimates across the marsh to the boundaries on the basis 

of travel distances along the marsh and in the open channels. 

Figure 3 shows the relation of the marsh boundary to the tide 

gate. This test was designed to model the height of a high tide 

at the boundary of the marsh with the tide gates open. Sybil 

Creek has two tide gates and one bridge constriction (fig. 5). 

The locations of these structures are shown on the infra-red 

photograph of the marsh (fig. 3), along with points of observed 

tide height (tables 1 and 2), and on figure 4.

In order to apply the model to any point in the marsh (and 

specifically to the boundary), a GIS method was developed 

to measure flow-path lengths and to estimate the amount of 

open water in the marsh. The open-water fraction along the 

flow paths was required so that the diffusive properties of the 

channel and open water could be considered separately from 

those in the marsh-grass regions of the marsh. The open-water 

fraction was estimated from three-band false color infrared 

orthophotography taken in the summer of 2005, which was 

provided by CTDEEP, using an image analysis software package MultiSpec (Landgrebe and Biehl, 2011). The software 

was used to distinguish between water and non-water (fig. 6) 

and was calibrated visually from selected representative areas 

of the orthophotography for classification. Areas of shadows 

appearing in the orthophotography were consistently identified 

as water by the program; these were removed manually.

The GIS was used to determine the marsh geometry and 

flow paths by first digitizing the centerline of the main channel 

within the marsh and then using a pre-existing geospatial dataset that defines the upland marsh boundary. From the channel 

centerline, perpendicular lines were constructed to the marsh 

boundary. The channel centerline was designed to allow perpendicular flow paths every 50 ft; however, the nature of the 

channel’s orientation precluded the use of every flow path. In 

instances where multiple paths intersected or where multiple 

paths of varying length converged to the same region of the 

upland boundary, the shortest-length path was retained.

The channel was assumed to be the primary flow path 

into the marsh, and the perpendicular lines were assumed 

to represent the idealized flow path from the channel to the 

marsh boundary, along which the tidal wave was propagated. 

Figure 6 illustrates the water-surface area determined by using 

MultiSpec analysis of the infrared orthophotography. Figure 7 

illustrates the flow paths, defined for the analysis, including 

the channel and perpendicular flow paths, as well as polygons 

that extend 25 ft on each side of the perpendicular lines. In 

order to classify the physical characteristics of the marsh in the 

region of the flow paths, the percentages of marsh and open 

water were determined for each of these polygons.

A spreadsheet was developed to compute (1) the estimated tide heights within the channel, as a function of distance 

from the tidal source and an assumed channel diffusivity, and 

(2) the estimated tide heights at the marsh boundary, as a function of the tide height at each channel node, the flow length 

through the marsh, and an assumed marsh diffusivity. The 

attenuation of the tide through the constriction was estimated 

by using the calibrated diffusivity for the tide gates and the 

bridge. The channel and marsh diffusivities were assumed to 

be constant with values of 5.00E-12 and 5.00E-09 day per 

square foot (day/ft2), respectively. These are representative 

values determined from the calibration for all of the marshes.

The highest spring tides typically occur in October, and 

these are often used to determine the limits of extreme high 

water. In tidal marshes, this boundary can be located in the 

field through careful interpretation of wracklines deposited 

beyond upland borders by high spring tides. It is important to 

use the most recent high-tide values rather than an average of 

the highest tides over the lunar nodal cycle because the hightide-line changes annually due to the metonic cycle and sealevel change. For this reason, the highest October spring tide 

for the three year period 2005 to 2007 was used for this study.
10 A One-Dimensional Diffusion Analogy Model for Estimation of Tide Heights in Selected Tidal Marshes in Connecticut

Tide Gates

Bridge

Sybil Creek

Marsh

Figure 4. Oblique photograph of Sybil Creek marsh, Connecticut, looking eastward from the mouth of Sybil Creek where it enters 

Branford Harbor, 2003. Courtesy of the Department of Energy and Environmental Protection, Bureau of Water Protection and Land 

Reuse, and the Office of Long Island Sound Programs.

Figure 5. The tide gate in closed position (left) and the bridge constriction (right) on Sybil Creek, Connecticut.
Method Validation and Application for Sybil Creek 11

987000 988000 989000

657000

656000 ®

0 250 500 FEET0 75 150 METERS

Base from 2005 Coastal Colorinfrared OrthoimageryState of Connecticut, Department of Energy & Environmental ProtectionScale: 1:12,000, Coordinate System: Connecticut State Plane (feet), Datum: NAD1983Projection: Lambert Conformal Conic, Central Meridian: -72.75Standard Parallel 1: 41.2, Standard Parallel 2: 41.866667

Sybil Creek study area boundary—

Photo interpreted about 1995

MultiSpec Output

Water-deepWater-shallowLand

EXPLANATION

Figure 6. Areas of water and non-water (land) resulting from MultiSpec analysis of the three-band false color infrared orthophotography of Sybil 

Creek marsh, Connecticut. Four different characteristic water spectra were found to provide the best representation of the water area in the marsh and were classified as shallow and deep. Areas of shadows identified as water by the program (visible near many of the homes) were removed manually from areas within the marsh boundary.
12 A One-Dimensional Diffusion Analogy Model for Estimation of Tide Heights in Selected Tidal Marshes in Connecticut

2.333

0.75

1.417

0.917

1.5

0.583 0.917

1.083

1.25

0.667

0.333

1.083

0.75

0

-0.667

0.917

3.667

1.333

0.167

0.33

0

3

.417

0.917

1.417

1.083

1.75 1.5

0.333 2.167 0.5

1.75

0.167

0.167

0.5

0.833

0.667

1.417

0.583

0.417

0

0.417

1.5

1.083

1

1.083

0.917

1.333

1.083

0.417

2.333

0.75

1.417

0.917

1.5

0.583 0.917

1.083

1.25

0.667

0.333

1.083

-0.5

0.75

0

-0.667

0.917

3.667

1.333

0.167

0.333

0.417

0.917

1.417

1.083

1.75 1.5

0.333 2.167 0.5

1.75

0.167

0.167

0.5

0.833

0.667

1.417

0.583

0.417

0

0.417

1.5

1.083

1

1.083

0.917

1.333

1.083

0.417

987000 988000 989000

657000656000

0 300 600 FEET

0 90 180 METERS

Base from 2005 Coastal Colorinfrared OrthoimageryState of Connecticut, Department of Energy & Environmental ProtectionScale: 1:12,000, Coordinate System: Connecticut State Plane (feet)Datum: NAD1983, Projection: Lambert Conformal ConicCentral Meridian: -72.75, Standard Parallel 1: 41.2Standard Parallel 2: 41.866667

Main channel points—50-foot spacingStudy boundary points—Number is elevation, in

 feet above NAVD 88

Sybil Creek study area boundary—

Photo interpreted about 1995

Main Channel—Stream centerlineMain Channel Perpendicular Flow Paths—

Non intersecting shortest paths

Flow Path Characteristic Regions—

25-foot buffer on either side

Water-deepWater-shallowLand

EXPLANATION

Figure 7. Geographic information system overlay of the Sybil Creek marsh, Connecticut, with the channel flow path, perpendicular flow paths 

from the channel to the marsh boundary, and the characteristic marsh polygons defined by buffering the perpendiculars and determined by using MutiSpec classification data.
Method Validation and Application for Sybil Creek 13

The model simulated high-tide heights for a normal 

(neap) tide, as observed during the Milone and MacBroom 

study (1987), and a design high tide. The simulations included 

conditions with the gates closed (existing condition with some 

leakage of water past the gates which do not close completely 

in some cases), one gate open, and both gates open. As there is 

no local tide gage, the tidal data for Branford (at the mouth of 

Sybil Creek), used in this study, were estimated by using data 

from the National Oceanographic and Atmospheric Agency 

(NOAA) tidal station in Bridgeport with a NOAA-provided 

correction factor. The highest October tide for 3 years (2005–

2007), estimated for Branford Harbor, was used for translation 

to the mouth of Sybil Creek. 

The application was compared to the one-gate-open test 

that was conducted by Milone and MacBroom (1987) during their study. This is the only case during which a gate was 

opened for a sufficient length of time to yield steady water 

levels in the marsh. All other observations made in the marsh 

were made with gates closed. Only one gate was opened to 

avoid inundating properties. The comparison between the 

observed and estimated tide heights for the one-gate-open condition showed a good match at the two observation points that 

were available within the modeled area. The observed heights 

(table 1) at P3 and S2m are 2.11 and 1.60 ft, respectively, 

and the GIS simulated heights are 2.04 and 1.55 ft above the 

National Geodetic Vertical Datum of 1929 (NGVD 29). Using 

these values, the estimated tide heights at the observation 

points measured by Milone and MacBroom (1987) for the 

one-gate-open condition were estimated to be within ±0.1 foot 

of the calibrated values. This indicates that the general values 

used for diffusivity in the calibration and transferred to the 

GIS application provide accurate results for different gate scenarios. Unfortunately, few points were available to calibrate or 

validate the method other than the points listed in tables 1 and 

2. For this reason, the estimates made at the boundary are considered to be approximate when used as a guide for regulatory 

action. Future work might include the development of buffer 

zones that are based on the approximate estimates developed 

by using this method, to account for uncertainty.

No validation data are available for the gates-open 

condition, except for those discussed above. The only 

validation data available for the GIS application of the 

method included general observations made during the pretest existing condition with both gates closed, as reported by 

Milone and MacBroom (1987). To use this data for validation, 

a diffusivity for the gates-closed condition was estimated 

from the calibration data set by matching the observed tide 

heights at P2 and P3 (see table 1). Using this value for the 

gate constriction in the spreadsheet application, heights at the 

marsh boundary were estimated and compared with observed 

values for the high-tide height and tidal range from the 

Milone and MacBroom study (1987). These tide values are 

listed in table 3. The spreadsheet-estimated tide height was 

within 0.3 ft of the observed height at P3. This comparison 

is not direct because the tidal range at the source for the P3 

gates-closed condition was not specified in the study and is 

an estimate.

The method presented here estimates a potential height 

relative to a datum (in this case the tide heights relative to 

mean sea level). Interpretation of the results requires comparison with the topographic limitations in the marsh. For example, the method may estimate a tide height at a given distance 

that is well below the topographic elevation at that location 

in the marsh. Under this circumstance, the tide is interpreted 

as not reaching the location, and thus for that tidal range, 

the marsh at that distance does not experience a tidal flux. 

Estimated tide heights for the gates-closed condition indicate 

that the tide does not extend into the marsh and is confined 

to the channel. This is evident from the marsh topography 

provided by Milone and MacBroom (1987), which shows that 

the heights of the marsh are greater than the estimated tide 

heights and also shows that the marsh ponds are isolated from 

the channel and the tide. On the basis of anecdotal observations (Richard Orson, Save The Sound, New Haven, Conn., 

personal commun., 2009), under normal operating conditions 

(gates closed) the tide does not leave the channel, and the 

ponds are isolated, qualitatively confirming the model results.

Table 3. Estimated tide heights and ranges at Sybil Creek, Connecticut, used in the model.

[NAVD 88, North American Vertical Datum of 1988; NGVD 29, National Geodetic Vertical Datum of 1929]

Tide description

Estimated high-tide height 

at Branford Harbor 

(feet)

Estimated tidal range 

at Branford Harbor 

(feet)

3-year (2005–2007) October high (NAVD 88) 4.8 8.2

Sybil Creek Study, Milone and MacBroom, 1987 (NGVD 29) 4.5 7

Sybil Creek Study, Milone and MacBroom, 1987 (NAVD 88) 3.5 7
14 A One-Dimensional Diffusion Analogy Model for Estimation of Tide Heights in Selected Tidal Marshes in Connecticut

Given the paucity of data for verification of the estimated 

tide heights, the existing condition estimates were compared 

with marsh heights derived from Light Detection And 

Ranging (LiDAR) data for coastal Connecticut in winter 2006 

(Connecticut Department of Environmental Protection, 2008). 

The difference between the estimated height and the LiDAR 

height at the marsh boundary plotted against the distance from 

the tidal source is shown in figure 8. The plot shows that the 

heights at the marsh boundary are greater than the estimated 

high-tide heights along the entire boundary, except near the 

tidal source. This indicates that the model is estimating tide 

heights within the correct range near the source, but farther 

away from the source, the marsh height is greater than the 

tide height. This confirms the expected result, in that the high 

tide would be expected to be contained within the marsh 

boundaries when the gates are closed.

The simulated tide heights at the marsh boundary for the 

existing gates-closed condition are shown in figure 8. Note 

that the LiDAR elevations are greater than the simulated 

tide heights for most of the marsh. The LiDAR-based marsh 

heights at the boundary are shown in figure 9. These heights 

do not necessarily document the water-surface height at high 

tide because of the time of the LiDAR data collection and 

interference from vegetation and irregular ground surface; 

however, given the attenuation of the tide through the gate and 

bridge, the heights are considered to be indicative of the water 

surface in the channel and the marsh surface at the boundary. 

The simulated potential tide heights at the boundary with both 

gates open are shown in figure 10. The heights are greater than 

the LiDAR elevations at the marsh boundary, indicating that 

if both gates were open, the entire marsh would be flooded up 

to 1 foot at the farthest distance from the tide gage. A comparison of the estimated heights with the 1987 topography 

from Milone and MacBroom (1987) indicates that a number of 

structures near the bridge at the western end of the study area 

would be flooded.

Limitations

The model presented here was designed to be a simple 

way to estimate tidal heights using only remote sensing or 

geographic information system data layers; therefore, it has 

several limitations. The model is not a complete representation 

of the marsh geometry, and because of the paucity and distribution of the data, the estimates made at the boundary of the 

marsh are considered to be approximate when used as a guide 

for regulatory actions. 

y = -0.0005x + 0.3261

R2

 = 0.2542

-4

-3

-2

-1

0

1

2

0 500 1,000 1,500 2,000 2,500 3,000 3,500

Difference between estimated and LiDAR heights

at marsh boundary, in feet 

Marsh distance from source, in feet

Figure 8. Difference between the estimated tide heights and LiDAR heights at Sybil Creek marsh, Connecticut, 

assuming gates closed and using a single point calibration, in relation to the distance from the source. The 

simulation with gates closed represents the existing condition that would be reflected by the LiDAR data.
Method Validation and Application for Sybil Creek 15

2.333

0.75

1.417

0.917

1.5

0.583 0.917

1.083

1.25

0.667

0.333

1.083

-0.5

0.75

0

-0.667

0.917

3.667

1.333

0.167

0.33

0

3

.417

0.917

1.417

1.083

1.75 1.5

0.333 2.167 0.5

1.75

0.167

0.167

0.5

0.833

0.667

1.417

0.583

0.417

0

0.417

1.5

1.083

1

1.083 0.917

1.333

1.083

0.417

2.333

0.75

1.417

0.917

1.5

0.583 0.917

1.083

1.25

0.667

0.333

1.083

-0.5

0.75

0

-0.667

0.917

3.667

1.333

0.167

0.333

0.417

0.917

1.083

1.417

1.75 1.5

0.333 2.167 0.5

1.75

0.167

0.167

0.5

0.833

0.667

1.417

0.583

0.417

0

0.417

1.5

1.083

1

1.083 0.917

1.333

1.083

0.417

987000 988000 989000

657000

656000

Base from 2005 Coastal Colorinfrared OrthoimageryState of Connecticut, Department of Energy & Environmental ProtectionScale: 1:12,000, Coordinate System: Connecticut State Plane (feet)Datum: NAD1983, Projection: Lambert Conformal ConicCentral Meridian: -72.75, Standard Parallel 1: 41.2Standard Parallel 2: 41.866667

0 300 600 FEET

0 90 180 METERS

Marsh boundary points—

Number is LiDAR-based marsh height,in feet above NAVD 88

Sybil Creek study area boundary—

Photo interpreted about 1995

EXPLANATION

Figure 9. LiDAR elevations at the boundary of the Sybil Creek marsh, Connecticut.
16 A One-Dimensional Diffusion Analogy Model for Estimation of Tide Heights in Selected Tidal Marshes in Connecticut

y = -0.001x + 3.9223

R2

 = 0.5912

-2

-1

0

1

2

3

4

5

6

0 500 1,000 1,500 2,000 2,500 3,000 3,500

Difference between estimated and LiDAR heights

at marsh boundary, in feet 

Marsh distance from source, in feet

Figure 10. Difference between simulated tide heights, assuming gates-open condition, and LiDAR heights at 

Sybil Creek marsh, Connecticut, in relation to the distance from the source. The simulation shows that the entire 

Sybil Creek marsh would be inundated up to approximately 1 foot at the farthest distance from the tide gates.

The model assumes that flow resistance does not change 

with head, implying that friction is uniform, which may not be 

reasonable for the full range of flow in the open channels and 

through constricted openings. Therefore, the model is calibrated only for a single high-tide level of interest; arrival times 

at lower tide heights may have substantial errors. In addition, 

the small data set available precluded a more in-depth analysis 

that could develop a general relation to characterize openings 

and diffusivity.

The one-dimensional diffusion analogy model should 

not be used to evaluate tide heights, flow velocities, and tide 

arrival times for tide conditions other than the highest tide 

for which it is calibrated. Additionally, because the model 

does not include depth or water-surface slope information, flow velocity, travel time, and tidal storage cannot be 

estimated reliably.

Summary and Conclusions

A study was conducted to develop a one-dimensional 

diffusion analogy model to estimate tide heights in four 

coastal marshes in Connecticut. The method used to estimate 

maximum tide heights in coastal marshes in this study can be 

used for areas where the high tides under specific conditions 

cannot be measured directly, such as marshes with tide gates 

that cannot be opened without risk of flooding properties and 

structures. The simplicity of the method allows it to be used 

to evaluate the tide heights in estuaries and marshes with 

significantly less field and modeling effort than other methods 

used for modeling marsh hydrodynamics. The method can 

be applied with limited calibration information that is based 

entirely on remote sensing or geographic information system data layers. Tide heights were estimated for four coastal 

marshes in Connecticut—Pine Creek, Sybil Creek, Leetes 

Island, and Wilson Cove marshes.

The model was calibrated and validated by using data 

collected during previous studies. The expected accuracy of 

the method is in the range ±0.1 to 0.3 foot (based on the error 

in the calibration/validation points for the marshes studied). 

The method would be applicable as a survey tool for assessing conditions along the coast and could be used to indicate 

those marshes with greatest potential for successful restoration 

without increasing flooding of existing structures and properties. Additionally, the method could be used to make a first 

estimate of tide heights, which would indicate where more 

detailed modeling would be needed.
References Cited 17

The method developed and tested in this study to 

estimate extreme high water limits in tidal marshes along 

the Connecticut coast can assist in regulatory and planning 

processes. The method provides a simple, consistent, and 

inexpensive way to estimate these boundaries where direct 

measurements are not possible and where direct measurements 

have not yet been made. The method is simpler to use than 

other one- and two-dimensional hydrodynamic models 

because it does not require marsh depth and tidal prism 

information; however, the one-dimensional diffusion analogy 

model cannot be used to evaluate tide heights, flow velocities, 

and tide arrival times for tide conditions other than the highest 

tide for which it is calibrated. Additionally, because the model 

does not include depth or water-surface slope information, 

flow velocity, travel time, and tidal storage cannot be 

estimated reliably. 

Acknowledgments

The authors would like to thank John Warner (USGS 

Woods Hole) and Robert Dudley (USGS New England Water 

Science Center Maine Office) for their helpful and insightful 

technical review and comments, and Ruth Larkins (USGS 

Science Publishing Network) and Virginia de Lima (USGS 

New England Water Science Center Connecticut Office) for 

helpful technical and editorial review comments.

References Cited

Adamowicz, S., and Roman, C.T., 2005, New England salt 

marsh pools—A quantitative analysis of geomorphic and 

geographic features: Wetlands, v. 25, no. 2, p. 279–288.

Coats, R., Swanson, M., and Williams, P., 1989, Hydrologic 

analysis for coastal wetland restoration: Environmental 

Management, v. 13, no. 6, p. 715–727.

Connecticut Department of Environmental Protection 

(CTDEEP), 2008, Original 2006 coastal LiDAR data, 

collected and processed by Terrapoint, Inc.; project 

managed by Dewberry, Inc.; QA/QC reviewed by Roald 

Haested, Inc., for FEMA under Task/Delivery Order 

Proposal Request “Riverine/Coastal Flood Studies” 

pursuant to CONTRACT NO. EME-2003-CO-0338: 

Connecticut Department of Environmental Protection.

Ferris, J.G., 1951, Cyclic fluctuations of the water-level as a 

basis for determining aquifer transmissivity: International 

Association of Scientific Hydrology Publication 33, 

p. 148–155.

Fischer, H.B., List, J.E., Koh, C.R., Imberger, J., and Brooks, 

N.H., 1979, Mixing in inland and coastal waters: Academic 

Press, 302 p.

Giannico, Guillermo, and Souder, J.A., 2004, The effects of 

tide gates on estuarine habitats and migratory fish: Oregon 

State University ORESU-G-04-002, 9 p.

Landgrebe, D., and Biehl, L., 2011, MultiSpec version 9.2011: 

School of Electrical and Computer Engineering, Purdue 

University, Purdue Research Foundation, 189 p., accessed at 

https://engineering.purdue.edu/~biehl/MultiSpec/.

Milone and MacBroom Consulting Engineers, 1987, Sybil 

Creek salt marsh study, Branford, Conn.: Connecticut 

Department of Environmental Protection.

Milone and MacBroom Consulting Engineers, 1999a, Leetes 

Island marsh, Guilford, Conn., prepared the Connecticut 

Department of Environmental Protection Office of Long 

Island Sound.

Milone and MacBroom Consulting Engineers, 1999b, Wilson 

Cove tidal restoration, Norwalk, Conn.: City of Norwalk, 

Conn.

Roman, C.T., Garvine, R.W., and Portnoy, J.W., 1995, 

Hydrologic modeling as a predictive basis for ecological 

restoration of salt marshes: Environmental Engineering, 

v. 19, no. 4, p. 559–566.

Roman, C.T., Niering, W.A., and Warren, R.S., 1984, Salt 

marsh vegetation change in response to tidal restriction: 

Environmental Management, v. 8, p. 141–150.

Todd, D.K., 1980, Groundwater hydrology: New York, John 

Wiley and Sons, 336 p.

Turner, I.L., Coates, B.P., and Acworth, R.I., 1996, The effects 

of tides and waves on water-table elevations in coastal 

zones: Hydrogeology Journal, v. 4, no. 2, p. 51–69.
Prepared by the Pembroke and West Trenton Publishing 

Service Centers.

For more information concerning this report, contact:

Office Chief

U.S. Geological Survey

New England Water Science Center

Connecticut Office

101 Pitkin Street

East Hartford, CT 06108

dc_ct@usgs.gov

or visit our Web site at:

http://ct.water.usgs.gov
Bjerklie and others—A One-Dimensional Diffusion Analogy Model for Estimation of Tide Heights in Selected Tidal Marshes in Connecticut—SIR 2013–5076